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The D-meson spectral density at finite temperature is obtained within a self-consistent coupled-channel approach. For the bare meson-baryon interaction, a separable potential is taken, whose parameters are fixed by the position and width of the Lambda_c (2593) resonance. The quasiparticle peak stays close to the free D-meson mass, indicating a small change in the effective mass for finite density and temperature. However, the considerable width of the spectral density implies physics beyond the quasiparticle approach. Our results indicate that the medium modifications for the D-mesons in nucleus-nucleus collisions at FAIR (GSI) will be dominantly on the width and not, as previously expected, on the mass.